On ϕ-Absorbing Primary Elements in Lattice Modules
Let L be a C-lattice and let M be a lattice module over L. Let ϕ:M→M be a function. A proper element P∈M is said to be ϕ-absorbing primary if, for x1,x2,…,xn∈L and N∈M, x1x2⋯xnN≤P and x1x2⋯xnN≰ϕ(P) together imply x1x2⋯xn≤(P:1M) or x1x2⋯xi-1xi+1⋯xnN≤PM, for some i∈{1,2,…,n}. We study some basic properties of ϕ-absorbing primary elements. Also, various generalizations of prime and primary elements in multiplicative lattices and lattice modules as ϕ-absorbing elements and ϕ-absorbing primary elements are unified.
2014 ◽
Vol 42
(6)
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pp. 2338-2353
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2020 ◽
Vol 23
(3)
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pp. 227-252
2012 ◽
Vol 132
(11)
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pp. 420-424
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